Well, in FS1 the Shivans appeared in early January 2335 (on 18th Jan we have the first mention of Shivans in the Command Briefing, not long after your first encounter with the SF Scorpions), and the destruction of Lucifer on 29th March (assuming that the pursue of the Lucy from the Delta Serpentis node to the Sol one didn't take longer than several hours).
It's harder to say about FS2, because there were no dates given, however, at the beginning of the campaign, we are told that the NTF rebellion has been ongoing for the past 18 months. And after being transferred to the GTV Psamtik, Admiral Khafre tells us that "we begin the process of rebuilding these systems after 18 months of bloodshed". This would mean, that between the time period between the destruction of the GTC Vigilant and the appearance of SJ Sathanas was about one month. That would correlate nicely with FS1, because the destruction of the Tombaugh station and the following appearance of Lucifer has happened about a month after the official confirmation of Shivan presence.
My guess is, that the SSI took about 2-3 months, about as long as the first one.